3D modeling geometry types

3D modeling tools actually rely on a handful of different geometry representations, each with strengths and trade-offs.

1. Meshes (polygonal modeling)

A shape represented by vertices, edges, and faces (usually triangles or quads).

• Common use: in games, visual effects, real-time rendering, 3D printing.
• Pros: Lightweight, fast to render, easy to manipulate and subdivide.
• Cons: Not inherently precise — curves are approximated by flat facets.

2. Boundary Representation (B-Rep)

A solid modeling approach where objects are defined by their boundaries (faces, edges, vertices) using exact mathematical surfaces.

• Common use: in CAD/CAM, engineering, manufacturing.
• Pros: High precision; supports Boolean operations, fillets, chamfers, etc.
• Cons: Heavier data structures, slower for visualization or games.

3. NURBS (Non-Uniform Rational B-Splines)

Mathematical curves and surfaces defined by control points, weights, and knots.

• Common use: in industrial design, automotive, aerospace, product design.
• Pros: Smooth, exact representation of curves and freeform surfaces.
• Cons: Complex to edit at large scale; not as efficient for polygon-based rendering pipelines.

4. Subdivision Surfaces (SubD)

A hybrid between mesh modeling and smooth surface modeling. A coarse control mesh is subdivided to generate smooth surfaces.

• Common use: Animation, character modeling, industrial design.
• Pros: Intuitive and artist-friendly; smooth results from simple meshes.
• Cons: Not exact like NURBS; requires careful topology.

5. CSG (Constructed Solid Geometry)

Solids are built from primitives (cubes, spheres, cylinders) using Boolean operations (union, subtract, intersect).

• Common use: parametric CAD, procedural modeling, scripting tools (OpenSCAD).
• Pros: Intuitive, parametric, easy for procedural workflows.
• Cons: Can produce messy geometry when converted to meshes or BREPs.

6. Parametric / Feature-Based Models

A higher-level layer on top of BREPs/CSG, where geometry is driven by parameters and history trees (e.g., “extrude this sketch 20mm”).

• Common use: CAD tools like SolidWorks, Fusion 360, Creo.
• Pros: Fully editable and reproducible; great for design iteration.
• Cons: Heavy and rigid compared to mesh workflows.

7. Point Cloud

A collection of discrete points in 3D space, often captured by scanners or photogrammetry.

• Common use: Reality capture, surveying, reverse engineering.
• Pros: Captures real-world detail quickly.
• Cons: Not directly usable for CAD/manufacturing until converted into meshes or surfaces.

8. Implicit / Volumetric Models

Instead of surfaces, the shape is defined by a function (e.g., all points where f(x,y,z)=0). Includes signed distance fields (SDFs) and voxel grids.

• Common use: Simulation, medical imaging, sculpting (ZBrush’s dynamesh, Blender’s remesh).
• Pros: Excellent for morphing, blending, and operations like smooth unions.
• Cons: Requires conversion to mesh or B-Rep for precise CAD or manufacturing.

9. Functional Representation (FRep)

A 3D object is defined by a single continuous function F(x,y,z).

• Examples:
  • The solid is the set of all points where F(x,y,z) ≥ 0.
  • Surfaces live at F(x,y,z)=0.
• Common use: Procedural/generative modeling in academic and research systems, medical imaging & biology, computer graphics research, fabrication research, and physics simulations
• Pros: Functions are compact and easy to store. Since it’s just math functions, you can define deformations, morphing between geometries, offsets, and even time-dependent shapes.
• Cons: Not widely supported, math-heavy, needs to be converted into a BRep for manufacturing, simulation, or 3D printing.